I use cold water.
Nothing else, and I tend to re-use my cleaning patches after a soak and wash.

After a full cold water patching and scrub with a fiber brush if necessary I oil with bear oil that I rendered from a coastal black bear.
I have no rust or pitting problems at all.

Holland and Holland still recommend plain water as the best cleaning solution for black powder guns and rifles.

As a note, I don't run corrosive priming compounds, and I don't run imitation 'black powder substitutes'

Cheers
Tinker